What is the solution of the systems of equations y=-3x-3 and y=-0.5x+2?

This is two lines in slope intercept form and we want their intersection. We just set the ys equal.

-3x - 3 = (-1/2) x + 2

Multiply both sides by 2 to clear the fractions,

-6x - 6 = - x + 4

-10 = 5x

x = - 10/5 = - 2

y = - 3x - 3 = - 3 (-2) - 3 = 6 - 3 = 3

Check:

y = (-1/2) x + 2 = (-1/2) (-2) + 2 = 1 + 2 = 3, good

Answer: x=-2, y=3